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POST UTME IMS U 2020 Mathematics | Objective

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Question 1 View Details

Find the derivative of the function ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ) using the chain rule.

A. \(\frac{-2x}{x^2 + 1\) \ ^2}\)\) )

Correct B. \(\frac{2x}{x^2 + 1\) \ ^2}\)\) )

C. \(\frac{2}{x^2 + 1\) \ ^2}\)\) )

D. \(\frac{-2}{x^2 + 1\) \ ^2}\)\) )

Correct Answer: B

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Question 2 View Details

Solve the inequality \(2^x > 3^x\) for ( x ).

Correct A. \(x < -1\)

B. \(x > -1\)

C. \(x < 1\)

D. \(x > 1\)

Correct Answer: A

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Question 3 View Details

A matrix ( A ) is given by \(A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}\). Find the determinant of ( A ).

A. ( 2 )

B. \(-2\)

Correct C. ( 0 )

D. ( 1 )

Correct Answer: C

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Question 4 View Details

A sequence is defined by \(a_n = 2n + 1\). Find the sum of the first 5 terms of the sequence.

A. ( 15 )

B. ( 20 )

Correct C. ( 25 )

D. ( 30 )

Correct Answer: C

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Question 5 View Details

A set ( S ) is defined as S = { x | x in mathbb{R}, \(x > 0\) }. Find the complement of ( S ).

Correct A. { x | x in mathbb{R}, x leq 0 }

B. { x | x in mathbb{R}, x geq 0 }

C. { x | x in mathbb{R}, \(x < 0\) }

D. { x | x in mathbb{R}, \(x > 1\) }

Correct Answer: A

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Question 6 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24π cm³

Correct B. 48π cm³

C. 96π cm³

D. 192π cm³

Correct Answer: B

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Question 7 View Details

Solve the inequality \(x^2 + 4x - 5 > 0\).

Correct A. \(x < -5\) or \(x > 1\)

B. \(x < -5\) or \(x < 1\)

C. \(x > -5\) or \(x > 1\)

D. \(x < -5\) or \(x = 1\)

Correct Answer: A

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Question 8 View Details

Find the equation of the circle with center \(-2, 3 \\) ) and radius 4.

Correct A. \(x + 2 \\)^2 + \(y - 3\)^\(2 = 16\) )

B. \(x - 2 \\)^2 + \(y + 3\)^\(2 = 16\) )

C. \(x + 2 \\)^2 + \(y + 3\)^\(2 = 16\) )

D. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 16\) )

Correct Answer: A

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Question 9 View Details

A particle moves along the curve (y = \(x^2\)\) with a velocity of 2 \(m/s\\((y = x^2) with a velocity of 2\). Find the acceleration at the point where \(x = 2\).

A. 4 \(m/s\)²

Correct B. 8 \(m/s\)²

C. 12 \(m/s\)²

D. 16 \(m/s\)²

Correct Answer: B

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Question 10 View Details

Find the area under the curve \(y = x^3 - 6x^2 + 9x + 2\) from \(x = 0\) to \(x = 4\).

A. 128

Correct B. 192

C. 256

D. 320

Correct Answer: B

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Question 11 View Details

Determine the value of (x\) in the equation \(\\((x) in the equation \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ 5 \end{bmatrix} = \begin{bmatrix} 3 \ 11 \end{bmatrix}\)

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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Question 12 View Details

A particle moves in a straight line with its position given by (s(t) = \(2t^3 - 5t^2 + 3t + 1\)\). Find the velocity of the particle at \(t = 2\\((s(t) = 2t^3 - 5t^2 + 3t + 1). Find the velocity of the particle at\) seconds.

A. -14

B. -10

Correct C. 10

D. 14

Correct Answer: C

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Question 13 View Details

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. \(1/2\)

Correct B. \(2/5\)

C. \(3/8\)

D. \(1/3\)

Correct Answer: B

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Question 14 View Details

Solve for (x\) in the equation \(\\((x) in the equation \log_{10} x^2\)\(= 4\)\).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 15 View Details

Find the surface area of the sphere with radius \(r = 4\) cm.

A. 32π

Correct B. 64π

C. 128π

D. 256π

Correct Answer: B

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Question 16 View Details

In a certain number base, the value of the digit 5 is represented as \(\overline{1011}_5\). What is the decimal equivalent of this number?

A. 21

Correct B. 25

C. 31

D. 35

Correct Answer: B

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Question 17 View Details

Solve for ( x ) in the equation \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 7 \ 10 \end{bmatrix}\).

A. 2

B. 3

Correct C. 4

D. 5

Correct Answer: C

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Question 18 View Details

Find the equation of the circle with center ( (2, 3) ) and radius 4.

Correct A. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 16\) )

B. \(x - 3 \\)^2 + \(y - 2\)^\(2 = 16\) )

C. \(x - 4 \\)^2 + \(y - 3\)^\(2 = 16\) )

D. \(x - 2 \\)^2 + \(y - 4\)^\(2 = 16\) )

Correct Answer: A

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Question 19 View Details

A rectangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its volume.

Correct A. 72

B. 80

C. 90

D. 96

Correct Answer: A

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Question 20 View Details

Two events, A and B, are independent. If P(A) = 0.4 and P(B) = 0.6, find P(\(A \cap B\)).

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 21 View Details

Find the determinant of the matrix [ egin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix} ].

A. 0

B. 1

C. 2

Correct D. 3

Correct Answer: D

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Question 22 View Details

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

Correct A. \(1/2\)

B. \(2/3\)

C. \(3/5\)

D. \(4/7\)

Correct Answer: A

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Question 23 View Details

Solve for x in the equation [ \\((x^2 + 4x + 4\)\(= 0\)\) ].

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 24 View Details

Find the value of [ \log_{10} \(x^2\)\(= 4\)].

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 25 View Details

In the diagram below, what is the value of x?

A. 30

Correct B. 60

C. 90

D. 120

Correct Answer: B

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